From a physical point of view, loudspeakers with a small membrane and a low depth are not able to generate a change in volume needed for the playback of low frequencies. Simply put, one can say that small speakers are unable to provide enough bass. One way to circumvent this problem is to use what is called a harmonic continuation which utilizes the psychoacoustic effect that our hearing system is able to detect and hence perceive a fundamental out of its harmonics even if the former is not present in the perceived signal.
Another possibility exists which uses an exact modelling of the used loudspeaker. If this modelling is possible, an element called mirror filter can be used, which is able to distort the input signal in advance so that in sum i.e., under consideration of the non-linear distortions of the loudspeaker, again a linear system is generated. In this way, the physical boundaries of the speaker can be extended towards lower frequencies. However, this method is much more complex and should be mentioned at this point only for the sake of completeness.
In most cases, the above-discussed principles are used which are based on the effect of harmonic continuation. All of the systems are non-linear and therefore cause distortions that have to be kept acoustically as low as possible. In the technical field, it is known that good results are obtained if the input signal is separated into the harmonic and percussive or transient signal component. Here, good results in terms of low acoustic artefacts are achieved when the harmonic continuation of the transient signal component is obtained with the aid of a non-linear function and if the harmonic signal component is obtained with the use of a phase vocoder. The appropriate non-linear function as well as the use of the phase vocoder for this purpose is known. However, in currently used systems, the methods for separating the signal into the harmonic signal component and the transient signal component suffer from a high computational effort and high memory needs.